If they give me the same sort of reaction to the acid then surely it's all likely to be a Herx reaction rather than gut irritation.
I like the way you're thinking. I was thinking in the same way (about 5 years ago). But it turned out that oregano oil is so irritating - beyond anything else I tried. The same applies to menthol oil (enteric-coated menthol oil - look that up how it works and what it is because it's something different from normal liquid menthol oil). I burnt my gut so terribly with these two, beyond description. And then, of course, I became allergic to them. So now even oregano spice is a problem.
Grapefruit seed extract has been sitting in the box for the last year, waiting for me to decide if I want to risk it again.
Have you had a stomach gastroscopy? This may show to some degree if you have gut irritation. Even better if you had a capsule endoscopy - which not only shows the stomach but also lower parts of the gut. But the cost is... ridiculous (I wonder if you could give me a number - if you find the price in GB - I'm curious).
So... these are the problems that seem not to have any good solution. It's rather a kind of a vicious circle.
But many people are successfully using antimicrobials like oregano oil...
How would I start dealing with my gut now?
1. Healing my gut. I used Culturelle and vegetable diet (decreases acid production, is not allergenic for me as meat is and it's easily digestible). Glutamine also kind of works (but barely) but it also makes me sleepy and wired at the same time. DGL licorice was good as well as slippery elm for this step, too.
2. Increasing the speed of passage of food. The best here (and the easiest and the cheapest way) is fasting - even intermittent. The first meal after intermittent fasting goes very fast.
I wouldn't use chemical agents that increase the speed of passage. In the long run - they are no good. You get used to them and they stop working.
Then I'd use some foods that increase speed - beets and carrots. They usually work if you can handle fiber.
Then Culturelle also increases speed. Sometimes even too much. In order to make it work, I pour the contents of the capsule out and take like 1/3 of the capsule before the meal.
Sauerkraut used to work for me very well in this respect (and it's very very cheap) but no more - I can't handle this kind of fiber now. Bear in mind that you start with 1/2 - 1 teaspoon daily - you treat it not as a meal but as a medicine...
3. Then I'd try to make the stomach environment more acidic.
Bear in mind that if your passage time is very long, this acid will end up burning your stomach wall, so that's why you have to start with the above steps first. Have you tried Betaine Hcl? This kind of worked for me but in the long run made me sleepy (betaine is a methyl group donor). But the taste of these pills (if you happen to taste them) is just terrible, though you have to live with it, of course.
4. Only after these 3 basic steps are done, I'd go any further. If these 3 steps help or just the opposite. This may include a more aggressive use of antimicrobials/antibiotics/anything.
I hope that you can see that these steps are constructed in this way so as not to make your gut more irritated. And these are very basic things to be done when you start the treatment. However, this guide is not complete. There are many simple and effective things that can be done and these will come to my mind in time, maybe I'll add them here. These things are quite commonly known, the only problem is to find the step where they fit in. Should you use them in the beginning, or only after some other treatment? The order of these steps is crucial here. Unfortunately, there is no simple step-by-step guide that starts from the simplest things. Either people are selling something (so they don't care) or confirm that something more aggressive (like oregano oil) works like a charm - and it makes you think that this has to be it - a miracle cure - so you start using it without thinking it over (been there). Well, it's just great that it works but the problem begins when it doesn't or causes very bad side effects.
Also doctors - gastrologists - are no good in this respect. All the gastrologists (like 3 of them + endoscope operators) that I've been to prescribed me with PPIs. First, they referred me to a gastroscopy which always showed some kind of irritation or gastritis or erosion so it was a simple call for them - PPIs. Even despite the fact that the last time (gastritis) I specifically said that I don't produce stomach acid at all and this irritation is caused by some kind of sensitivity/irritation/allergy. There was no talking to this doctor. Maybe in your area you have a better experience with doctors...